Projection Pursuit Algorithm Research Articles

Special issue linStat: sequential projection pursuit

Friedman and Tukey (1974, A projection pursuit algorithm for exploratory data analysis. IEEE Trans Comput. C-23:881–890), in their seminal paper, coined the term projection pursuit to denote a sequential classification method where data are projected onto the direction which best separates a cluster from the others. The detected cluster is then removed from the data and the procedure is repeated until no clusters are left. This paper implements their approach by an iterative algorithm based on kurtosis minimization and k-means clustering. The algorithm is initialized with the eigenvector associated with the smallest positive eigenvalue of the standardized fourth moment. The iterative step simplifies the multivariate minimization procedure to a bivariate one, which admits an analytical solution. The classification step is a simplified version of k-means clustering, where the data are unidimensional and only two groups are sought. The practical usefulness and the asymptotic properties of the proposed method are illustrated with simulated data.

Comprehensive Evaluation Model for Urban Water Security: A Case Study in Dongguan, China

Water security plays a critical role in the development and stability of a region. Constructing an objective and reasonable evaluation indicator system is beneficial to quantitatively evaluating the regional water security status and improving water resource management. In this paper, an urban water security indicator system was established based on the Driving–Pressure–State–Impact–Response (DPSIR) framework with Dongguan City as a case study. By introducing the projection pursuit (PP) algorithm, a DPSIR–PP model was developed to quantitatively evaluate urban water security. The evaluation results show that Dongguan City’s water security index had an overall upward trend during the 13th Five-Year Plan period, with the evaluation grade rising from IV to III. The indicators with the top five weights are: river water quality condition, ecological index, the leakage rate of water supply network, the value added by industry, and the Dongjiang water resources development and utilization rate. The evaluation results are essentially in line with the reality of Dongguan City. On this basis, the internal links of water security and future trends were further analyzed. Through the evaluation results and policy analysis, it is shown that the water security-related measures implemented during the 13th Five-Year Plan period have been effective. Overall, the methodology proposed in this study is beneficial for gaining an in-depth understanding of urban water security impact factors and provides some theoretical basis and reference for future water resources management.

Ecological environment health assessment of lake water ecosystem system based on simulated annealing-projection pursuit: A case study of plateau lake

• A DPSR framework model was proposed and covers 26 multi-scale indexes. • Ecosystem health assessment was built from environment, ecology and socioeconomic system. • Ecological health, environmental pollution and water resources were combined to system. • Simulated annealing projection pursuit was introduced as assessment method. • The key factors affecting the Ecological environment health were identified. A lake ecological environment health assessment index system is constructed based on DPSR (Driving forces-Pressure-State-Responses) framework. The simulated annealing projection pursuit (SA-PP) algorithm, which can analyze high-dimensional data, is introduced and provides a new way for lake ecological environment health evaluation and decision-making. Qionghai, a typical plateau lake in Sichuan, China, is taken as an example to introduce the application of this assessment system. The results suggest the water ecological environment of Qionghai basin is in a relatively healthy state from 2017 to 2020. The state subsystem has the largest weight, and the important influencing factors affecting the health of lake water ecological environment are the water environment characteristics, ecological characteristics and pressure subsystem in the State subsystem. Zooplankton Simpson diversity index, chlorophyll a, NH 3 -N and total nitrogen are the main influencing factors of lake ecosystem health in the lake ecosystem health system. The restriction factor of the pressure subsystem is per capita daily domestic water consumption. Therefore, improving water quality and controlling water consumption intensity become important factors to improve the health of water resources and water environment in Qionghai basin. This study provides a new way for lake ecological environment health evaluation and decision-making.

Modal clustering on PPGMMGA projection subspace

SummaryPPGMMGA is a projection pursuit (PP) algorithm aimed at detecting and visualising clustering structures in multivariate data. The algorithm uses the negentropy as PP index obtained by fitting Gaussian mixture models (GMMs) for density estimation and, then, exploits genetic algorithms (GAs) for its optimisation. Since the PPGMMGA algorithm is a dimension reduction technique specifically introduced for visualisation purposes, cluster memberships are not explicitly provided. In this paper a modal clustering approach is proposed for estimating clusters of projected data points. In particular, a modal EM algorithm is employed to estimate the modes corresponding to the local maxima in the projection subspace of the underlying density estimated using parsimonious GMMs. Data points are then clustered according to the domain of attraction of the identified modes. Simulated and real data are discussed to illustrate the proposed method and evaluate the clustering performance.

Erratum: Water Practice and Technology 17 (3), 763–783: Assessment of karst water quality and analysis of pollution sources with a projection pursuit algorithm in Jinan spring area, China, Miao Yu, Xuerui Xing, Liting Xing, Zhenhua Zhao and Changsuo Li, https://doi.org/10.2166/wpt.2022.011

Erratum: <i>Water Practice and Technology</i> 17 (3), 763–783: Assessment of karst water quality and analysis of pollution sources with a projection pursuit algorithm in Jinan spring area, China, Miao Yu, Xuerui Xing, Liting Xing, Zhenhua Zhao and Changsuo Li, https://doi.org/10.2166/wpt.2022.011

Assessment of karst water quality and analysis of pollution sources with a projection pursuit algorithm in Jinan spring area, China

Abstract Karst water is one of the main drinking water sources in North China. The single factor method and projection pursuit algorithm (PPA) are employed to assess the karst water quality of the Baotu spring area in Jinan. The water quality distribution pattern, its causes, and the main groundwater pollution sources are analyzed. The water quality evaluation results of the PPA model are more reliable than those of the single factor method because the PPA model comprehensively considers the weight and correlation of various factors. The water quality of the study area is generally excellent, but the NO3− index content is high. In recent years, the water quality grades have been mainly class II ∼ class IV. The driving factors of water quality evolution are not only human activities, including artificial recharge, but also natural factors, such as carbonate mineral dissolution. These factors control both the distribution and evolution trend of water quality. Urban nonpoint sources have a significant impact on groundwater quality. Based on the current water quality situation, it is urgent to strengthen protection of the ecological environment in the southern recharge area of the spring region and the water quality control in the western region.

On the Coupling and Coordination Development between Environment and Economy: A Case Study in the Yangtze River Delta of China.

The coupling and coordination development of the environment and economy (CC2E) is one of the most vital issues to sustainable development. This paper adopted the coupling coordination model, projection pursuit algorithm, and random forest model to explore the spatial-temporal evolution and influencing factors of the CC2E in the Yangtze River Delta from 2015 to 2019, respectively. The results showed that: (1) The degree of coupling coordination (DCC) of the CC2E in most cities of the Yangtze River Delta has risen from primary coordination to intermediate coordination. (2) In the spatial perspective, the distribution of DCC is correlated with geographical location. The value of DCC in the western region was significantly lower than that of the eastern cities. (3) The influencing factors results showed that the GDP in the economic subsystem and the annual average concentration of PM2.5 in the environmental subsystem were the most influencing factors of DCC in the Yangtze River Delta. The established index system of CC2E and the measurements of CC2E provide a new idea for how to achieve sustainable development. Meanwhile, this study can provide recommendations for formulating the environmental protection and economic development policy.

Research on Outlier Detection for High-Dimensional Data Based on PPCLOF

Aiming at the “dimension disaster” problem encountered in the outlier detection of high-dimensional data, this paper uses the projection pursuit algorithm to perform non-linear dimensionality reduction on high-dimensional data by calculating the phase relationship between dimensions. According to the sample points obtained by dimensionality reduction, the LOF (Local Outlier Factor) algorithm is applied to calculate the outlier factor to obtain the relevant outlier data. In order to improve the calculation accuracy and efficiency of the LOF algorithm, clustering method is used to cut the outlier calculation data to reduce the amount of calculation. Experiments on real-world and artificial datasets, compared with the existing algorithms, demonstrated the effectiveness and efficiency of the proposed algorithm.

Research on Safety Evaluation Method of Integrated Optical Storage and Charging Station

This paper studies the correlation between charging process performance indicators and charging safety of Solar-Energy storage-Charge station, analyses the influence of environmental factors, technical factors, design factors, management factors and user factors on charging process safety of energy stations. The projection pursuit algorithm is used to evaluate the influence degree of each parameter on the safety of charging process; through the establishment of charging safety evaluation system, the safety risks of battery damage and even fire caused by excessive charging current and high battery temperature are identified. The monitoring parameters corresponding to the charging safety state are determined. According to the different battery types adopted by different vehicle models, the corresponding charging mode is determined. According to the monitoring results of key data of the core equipment in the charging process, such as charging current, charging voltage, battery temperature, etc., the charging strategies of different vehicle models and different battery types are analysed, which provides reference for the safe operation of charging process.

Projection pursuit algorithms to detect outliers

In this paper, we compare the methods proposed by Peña and Prieto (2001), and Filzmoser, Maronna, and Werner (2008) to detect outliers in a set of Argentine companies that quote their shares in the Stock Exchange. A significant heterogeneity between observations can be a consequence of the presence of outliers. The detection of outliers is an important task for the statistical analysis since they distort descriptive measures and parameters estimators. There are different multivariate methods to detect outliers, such as distance-based methods and projection pursuit methods.

Assessing the sustainability of renewable energy: An empirical analysis of selected 18 European countries.

There are many studies on the sustainability of renewable energy, mainly focusing on energy supply, economic, social, environmental and technological aspects, but there are few studies on the sustainability of renewable energy itself. This work focuses on the systematic and quantitative assessment of the sustainability of renewable energy itself by analyzing the sustainability of renewable energy in selected 18 European countries from 2007 to 2016. The consumption of renewable energy in these selected 18 countries accounts for ~95% of the consumption of renewable energy in the European Union. To scientifically evaluate the sustainability of renewable energy, 17 indicators are selected based on the energy-economy-environment theory. In order to deal with the high-dimensional, non-normal, and nonlinear complex data, and to assess the sustainability of renewable energy without standards, the projection pursuit algorithm and the real-coded accelerating genetic algorithm are combined to establish a comprehensive model to assess the sustainability of renewable energy. The results show that (i) the sustainability of renewable energy in Germany, the UK, France, and Italy is better than that in the other investigated countries; (ii) in the 17 indicators selected by the energy-economy-environment model, the factors of total energy demand, energy taxes, carbon dioxide emissions, sulfur oxides emissions, and nitrous oxides emissions exert a stronger impact on the sustainability of renewable energy; (iii) time-series analysis show that the general sustainable level is a wave of growth. Moreover, the proposed comprehensive model can effectively deal with the high-dimensional, non-normal, and nonlinear complex data, thus providing a feasible method for the quantitative analysis and evaluation of the sustainability of renewable energy.

Projection Pursuit Based on Gaussian Mixtures and Evolutionary Algorithms

We propose a projection pursuit (PP) algorithm based on Gaussian mixture models (GMMs). The negentropy obtained from a multivariate density estimated by GMMs is adopted as the PP index to be maximized. For a fixed dimension of the projection subspace, the GMM-based density estimation is projected onto that subspace, where an approximation of the negentropy for Gaussian mixtures is computed. Then, genetic algorithms are used to find the optimal, orthogonal projection basis by maximizing the former approximation. We show that this semiparametric approach to PP is flexible and allows highly informative structures to be detected, by projecting multivariate datasets onto a subspace, where the data can be feasibly visualized. The performance of the proposed approach is shown on both artificial and real datasets. Supplementary materials for this article are available online.

Gold Price Forecasting Based on Projection Pursuit and Neural Network

Gold price has significant nonlinear, time-varying, many influence factors and more difficult to determine. In order to improve the precision of forecast gold price, this paper proposes a gold price combination forecasting model based on pursuit algorithm and neural network. Firstly, projection pursuit algorithm is used to choose the influence factors, and then the selected impact factors are used as BP neural network input variables to learn and establish gold price forecast model, finally forecast performance is tested by simulation experiments. The test results show that combined model can well depict the gold price trend, simplify network structure, accelerate the network learning speed, and improve the prediction accuracy of gold price. It provides a new forecast method for gold price.

Defect localisation and quantitative identification in multi-layer conductive structures based on projection pursuit algorithm

ABSTRACTPulsed eddy current (PEC) technology has become a burgeoning method for detection and analysis of multi-layer conductive structures owing to rich time and frequency domain information presented by PEC signals. In this study, PEC technique is applied to characterise hidden-defect parameters while nondestructively inspecting multi-layer structures. A projection pursuit (PP) feature extraction method based on the information divergence index is investigated to effectively analyse PEC signals. An improved accelerating genetic algorithm is adopted to find the optimal projection direction. The signal’s dimension is reduced with minimal information loss while the data’s structure is preserved to the greatest degree. The features extracted on the basis of PP are simultaneously employed in crack localisation and crack length quantitative evaluation combined with a SVM classifier. The theoretical analysis and experimental results demonstrate that compared with the principal component analysis method, the features extracted by the presented PP algorithm work better for simultaneously characterising crack’s depth and size information and it reflect the inherent laws of the data, which make the features more physically interpretation meanwhile. Inversion accuracy for smaller and deeper cracks is enhanced obviously which will be helpful for crack localisation and quantitative identification of crack parameters in difficult situations.

An Intrusion Detection Model Based On Danger Theory for Wireless Sensor Networks

This paper, due to the intrusion detection problem in Wireless Sensor Networks, proposes an intrusion detection model based on the Danger Theory instead of the traditional Self-NonSelf theory. The intrusion detection model has two layers structure including danger perception and control decision, and it uses a multi-node cooperation mechanism. The perception node can realize the danger perception with Projection Pursuit Algorithm, and the decision node can detect the intrusion in detail with Extreme Learning Machine Algorithm. The logic process between their layers is consistent with the Danger Theory. The proposed model can realize the data trust between nodes with the Beta distribution trust evaluation method. By the simulations in the MATLAB, the proposed intrusion detection model on the whole is better than the SNS model at the aspects including classification training, danger perception, false negative rate, false positive rate and energy consumption.

ECHO SIGNAL SEPARATION USING ICA PROJECTION PURSUIT ALGORITHM

In any RADAR system, the foremost challenge is to identify the target echo signal from the mixture of unwanted echoes called clutter. RADAR equipment generates linearly frequency modulated pulses which when reflected back gives the information about the target’s range, location and velocity of approach. A significant amount of clutter introduced in RADAR signal is generated by the surface of sea. This surface type of clutter is modelled as Weibull noise source which is mixed with target echo. These are treated as two independent sources. Assuming that the echo signals are independent from each other and are non-Gaussian in nature we use Independent Component Analysis’s Projection Pursuit Algorithm to separate the components so that these components can be analyzed further for target detection an ranging.

A Method for Evaluating Sea Dike Safety

To implement the maintenance and management of the sea dike engineering, the qualitative factors and quantitative factors need to be combined to evaluate the sea dike safety. Firstly, the evaluation index system and evaluation grading criterions of sea dike safety are established. Secondly, a new weight structure of evaluation indexes is proposed to combine the subjective weight and objective weight. Fuzzy Analytic Hierarchy Process method is used to determine the subjective weight and implement the qualitative analysis for sea dike safety. Projection Pursuit algorithm is introduced to calculate the objective weight and implement the quantitative analysis for sea dike safety. Based on the minimum relative information entropy principle, above two weights are combined. Thirdly, an evaluation model of sea dike safety is built with the improved Set Pair Analysis method. Finally, the proposed analysis method is used to assess one sea dike safety in China. It is shown that the combined weight can describe both the subjective information of expert experience and objective variation information of samples values, the uncertainty of information can be handled by the improved Set Pair Analysis method. The evaluation model has the clear physical concepts and intuitive modeling process. The calculation result is reasonable. The proposed method can be applied to sea dike safety evaluation and other complex systems evaluation as well.

Coherency Identification in Large-Scale Power System Using Measured Data

This paper presents a new method to identify coherent generator groups in power system based on projection pursuit. Projection pursuit algorithm is introduced to model wide-area measured time series and analyses high-dimensional data in low-dimensional subspace. It could seek and extract key projection vectors reflecting generator coherent features and identify the coherency of generators according to projection directions of generators. The presented technique could realize real-time identification of coherent generators, in which grouping is based on measured data avoiding the impact of model parameters. It proves that the composition of principal components has corresponding relationship with system oscillation mode. Finally, China Southern Power Grid is used as testing system to verify the feasibility and effectiveness of the method.

Improved Genetic Projection Pursuit Method Based on Measured Data on Power Quality Comprehensive Evaluation of the Application

This paper uses Multi-index to assess regional power quality comprehensively. This paper introduces genetic projection pursuit method on power quality comprehensive evaluation. Without human intervention, this method overcomes the traditional power quality comprehensive evaluation method is influenced by subjective factors. Based on this, we put forward improved genetic projection pursuit algorithm. In the process of projection pursuit model and in the field data, changing the maximum normalized to normalization of national standard limit. According to the field experiment data in QingHai province, we assess the results by analysis and comparison with the original method. The improved method is more accurate on power quality comprehensive assessment.

Short-Term Power Forecasting of Small-Scale Hydropower Based on Projection Pursuit Algorithm

Compared with other traditional energy, the small-scale hydropower which is intermittent energy can not be stored and scheduled. The greater fluctuant of the output power of small-scale hydropower leads to great difficult to the operation of the power system. Most of the existing small-scale hydropower forecasting is considered as the load forecasting factors, and there is not effective forecasting method. This paper establishes an output power forecasting model of the small-scale hydropower based on Projection Pursuit. The simulation results show that the new algorithm has a strong practical application in the small-scale hydropower output power forecasting and the forecast accuracy meets the scheduling requirements.